write the linear equation in slope - intercept form.
1. $4x + y = 10$ 2. $3x - y = 7$ 3. $-2x + 3y = 12$

graph the linear equation.
4. $2x - 3y = 6$ 5. $5x - 3y = 15$ 6. $3x + 4y = 18$

(graphs for problems 4 - 6 are shown as coordinate grids)

match the equation with its graph.
7. $-9x + 3y = 0$ 8. $4x - 6y = 12$ 9. $25x - 10y = -50$
a. (graph of a line) b. (graph of a line) c. (graph of a line)

10. your friend finds the x - intercept of $4x - 5y = 20$.
is your friend correct? explain your reasoning.
$\begin{align*}4x - 5y &= 20\\4(0) - 5y &= 20\\-5y &= 20\\y &= -4\end{align*}$

Question

write the linear equation in slope - intercept form.
1. $4x + y = 10$  2. $3x - y = 7$  3. $-2x + 3y = 12$

graph the linear equation.
4. $2x - 3y = 6$  5. $5x - 3y = 15$  6. $3x + 4y = 18$

(graphs for problems 4 - 6 are shown as coordinate grids)

match the equation with its graph.
7. $-9x + 3y = 0$  8. $4x - 6y = 12$  9. $25x - 10y = -50$
a. (graph of a line)  b. (graph of a line)  c. (graph of a line)

10. your friend finds the x - intercept of $4x - 5y = 20$.
is your friend correct? explain your reasoning.
$\begin{align*}4x - 5y &= 20\\4(0) - 5y &= 20\\-5y &= 20\\y &= -4\end{align*}$

Accepted Answer

### Problem 1: $4x + y = 10$ in slope - intercept form ($y=mx + b$)
# Explanation:
## Step 1: Isolate $y$
Subtract $4x$ from both sides of the equation $4x + y=10$.
$y=- 4x + 10$
# Answer: $y=-4x + 10$

### Problem 2: $3x-y = 7$ in slope - intercept form
# Explanation:
## Step 1: Isolate $y$
Subtract $3x$ from both sides: $-y=-3x + 7$.
Multiply both sides by $- 1$ to get $y = 3x-7$.
# Answer: $y = 3x-7$

### Problem 3: $-2x + 3y=12$ in slope - intercept form
# Explanation:
## Step 1: Isolate $y$
Add $2x$ to both sides: $3y=2x + 12$.
Divide both sides by $3$: $y=\frac{2}{3}x + 4$.
# Answer: $y=\frac{2}{3}x + 4$

### Problem 4: Graph $2x-3y = 6$
# Explanation:
## Step 1: Find intercepts
For $x$ - intercept, set $y = 0$: $2x-3(0)=6\Rightarrow2x=6\Rightarrow x = 3$. So the $x$ - intercept is $(3,0)$.
For $y$ - intercept, set $x = 0$: $2(0)-3y=6\Rightarrow-3y=6\Rightarrow y=-2$. So the $y$ - intercept is $(0, - 2)$.
## Step 2: Plot points and draw line
Plot the points $(3,0)$ and $(0,-2)$ on the coordinate plane and draw a straight line through them.
# Answer: The line passes through $(3,0)$ and $(0, - 2)$ (graphing steps as above)

### Problem 5: Graph $5x-3y = 15$
# Explanation:
## Step 1: Find intercepts
For $x$ - intercept, set $y = 0$: $5x-3(0)=15\Rightarrow5x=15\Rightarrow x = 3$. So the $x$ - intercept is $(3,0)$.
For $y$ - intercept, set $x = 0$: $5(0)-3y=15\Rightarrow-3y=15\Rightarrow y=-5$. So the $y$ - intercept is $(0,-5)$.
## Step 2: Plot points and draw line
Plot the points $(3,0)$ and $(0,-5)$ on the coordinate plane and draw a straight line through them.
# Answer: The line passes through $(3,0)$ and $(0, - 5)$ (graphing steps as above)

### Problem 6: Graph $3x + 4y=18$
# Explanation:
## Step 1: Find intercepts
For $x$ - intercept, set $y = 0$: $3x+4(0)=18\Rightarrow3x=18\Rightarrow x = 6$. So the $x$ - intercept is $(6,0)$.
For $y$ - intercept, set $x = 0$: $3(0)+4y=18\Rightarrow4y=18\Rightarrow y=\frac{9}{2}=4.5$. So the $y$ - intercept is $(0,4.5)$.
## Step 2: Plot points and draw line
Plot the points $(6,0)$ and $(0,4.5)$ on the coordinate plane and draw a straight line through them.
# Answer: The line passes through $(6,0)$ and $(0,4.5)$ (graphing steps as above)

### Problem 7: Match $-9x + 3y=0$ with its graph
# Explanation:
## Step 1: Rewrite in slope - intercept form
$-9x + 3y=0\Rightarrow3y=9x\Rightarrow y = 3x$. The line passes through the origin $(0,0)$ and has a slope of $3$.
Looking at the graphs, Graph C passes through the origin and has a steep positive slope (consistent with $y = 3x$).
# Answer: C

### Problem 8: Match $4x-6y = 12$ with its graph
# Explanation:
## Step 1: Rewrite in slope - intercept form
$4x-6y=12\Rightarrow-6y=-4x + 12\Rightarrow y=\frac{2}{3}x-2$.
The $y$ - intercept is $-2$ and the slope is $\frac{2}{3}$. Graph A has a $y$ - intercept of $-2$ (or close to it) and a slope of $\frac{2}{3}$ (rise over run).
# Answer: A

### Problem 9: Match $25x-10y=-50$ with its graph
# Explanation:
## Step 1: Rewrite in slope - intercept form
$25x-10y=-50\Rightarrow-10y=-25x - 50\Rightarrow y=\frac{5}{2}x + 5$.
The $y$ - intercept is $5$ and the slope is $\frac{5}{2}$. Graph B has a $y$ - intercept of $5$ and a steep positive slope (consistent with $y=\frac{5}{2}x + 5$).
# Answer: B

### Problem 10: Analyze friend's $x$ - intercept calculation for $4x-5y = 20$
# Explanation:
## Step 1: Recall $x$ - intercept definition
To find the $x$ - intercept, we set $y = 0$, not $x = 0$. The friend set $x = 0$ (which is for finding the $y$ - intercept).
## Step 2: Correct calculation
Set $y = 0$ in $4x-5y = 20$: $4x-5(0)=20\Rightarrow4x=20\Rightarrow x = 5$. So the $x$ - intercept is $(5,0)$, and the friend's calculation is incorrect.
# Answer: The friend is incorrect. To find the $x$ - intercept, set $y = 0$ (not $x = 0$). The correct $x$ - intercept is $x = 5$ (point $(5,0)$).

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QUESTION IMAGE

Question

Explanation:

Problem 1: \(4x + y = 10\) in slope - intercept form (\(y=mx + b\))

Step 1: Isolate \(y\)

Step 1: Isolate \(y\)

Step 1: Isolate \(y\)

Answer:

Problem 2: \(3x-y = 7\) in slope - intercept form