Question

put it all together: 5.1/5.2 creating linear equations
1.) write 3x + 4y = 12 in slope - intercept form.
2.) write y = 5/12x - 1/2 in standard form.
3.) write y - 4 = 1/2(x - 3) in slope - intercept form.
4.) part a
consider the line that passes through (-1,4) and has a slope of - 2. which form of a linear equation is easiest for writing an equation of the line?
a. slope - intercept form b. point - slope form c. standard form
part b
select all the equations for the line that passes through (-1,4) and has a slope of - 2.
y - 4 = - 2(x - 1)
y - 4 = - 2(x + 1)
y = - 2x - 4
y = - 2x + 2
2x + y = 2

• 2x + 4y = - 1

5.) part a
consider the line that passes through (5,-2) and (0,18). which form of a linear equation is easiest for writing an equation of the line?
a. slope - intercept form
b. point - slope form
c. standard form
part b
select all the equations for the line that passes through (5,-2) and (0,18).
y + 2 = - 4(x - 5)
x + 4y = - 12
y - 6 = - 4(x + 1)
y = - 4x - 12
y = - 4x + 18
4x + y = 18

Explanation:

Step1: Rewrite $3x + 4y=12$ in slope - intercept form

Isolate $y$. Subtract $3x$ from both sides: $4y=-3x + 12$. Then divide by 4: $y=-\frac{3}{4}x+3$.

Step2: Rewrite $y=\frac{5}{12}x-\frac{1}{2}$ in standard form

Multiply through by 12 to clear the fractions: $12y = 5x-6$. Rearrange to get $5x-12y=6$.

Step3: Rewrite $y - 4=\frac{1}{2}(x - 3)$ in slope - intercept form

Distribute on the right side: $y-4=\frac{1}{2}x-\frac{3}{2}$. Add 4 to both sides: $y=\frac{1}{2}x-\frac{3}{2}+4=\frac{1}{2}x+\frac{5}{2}$.

Step4: Part A of 4

Given a point $(-1,4)$ and slope $m = - 2$, the point - slope form $y - y_1=m(x - x_1)$ is easiest. So the answer is B.

Step5: Part B of 4

Using point - slope form $y - y_1=m(x - x_1)$ with $x_1=-1,y_1 = 4,m=-2$, we get $y - 4=-2(x + 1)$.
Expand it: $y-4=-2x-2$, then $y=-2x + 2$. In standard form, $2x+y=2$.
So the correct equations are $y - 4=-2(x + 1)$, $y=-2x + 2$, $2x + y=2$.

Step6: Part A of 5

First find the slope $m=\frac{y_2-y_1}{x_2-x_1}=\frac{18+2}{0 - 5}=\frac{20}{-5}=-4$. Since we know the $y$-intercept is 18 (the point $(0,18)$), slope - intercept form $y=mx + b$ is easiest. So the answer is A.

Step7: Part B of 5

Using point - slope form with the point $(5,-2)$ and $m=-4$, we have $y+2=-4(x - 5)$.
Expand: $y+2=-4x + 20$, so $y=-4x+18$. In standard form, $4x + y=18$.
So the correct equations are $y + 2=-4(x - 5)$, $y=-4x + 18$, $4x + y=18$.

Answer:

1. $y=-\frac{3}{4}x + 3$
2. $5x-12y=6$
3. $y=\frac{1}{2}x+\frac{5}{2}$
4. Part A: B. Point - slope form

Part B: $y - 4=-2(x + 1)$, $y=-2x + 2$, $2x + y=2$

1. Part A: A. Slope - intercept form

Part B: $y + 2=-4(x - 5)$, $y=-4x + 18$, $4x + y=18$