Question

graph the linear equation, then use the graph to identify the x-intercept.

1. $-\frac{3}{4}x + y = -6$

$m = \underline{quadquad}$, $b = \underline{quadquad}$
$x$-intercept = $\underline{quadquad}$

1. $\frac{1}{2}y + x = -5$

$m = \underline{quadquad}$, $b = \underline{quadquad}$
$x$-intercept = $\underline{quadquad}$

1. $y + \frac{3}{4}x = 6$

$m = \underline{quadquad}$, $b = \underline{quadquad}$
$x$-intercept = $\underline{quadquad}$

1. $4y - 8x = 16$

$m = \underline{quadquad}$, $b = \underline{quadquad}$
$x$-intercept = $\underline{quadquad}$

1. the equation that represents the length $y$ (in inches) of jenna’s hair after $x$ months is represented by the equation $y = 0.75x + 12$.

a. graph the equation.
b. interpret the graph.
the $y$-intercept represents $\underline{quadquad}$
the slope shows $\underline{quadquad}$

Explanation:

Problem 12: $-\frac{3}{4}x + y = -6$

Step 1: Convert to slope - intercept form ($y = mx + b$)

We start with the equation $-\frac{3}{4}x + y=-6$. To get it in the form $y = mx + b$, we add $\frac{3}{4}x$ to both sides of the equation.
So, $y=\frac{3}{4}x - 6$.
In the slope - intercept form $y = mx + b$, $m$ is the slope and $b$ is the y - intercept. So, $m=\frac{3}{4}$ and $b = - 6$.

Step 2: Find the x - intercept

The x - intercept is the value of $x$ when $y = 0$. We substitute $y = 0$ into the equation $y=\frac{3}{4}x-6$.
We get $0=\frac{3}{4}x - 6$.
First, add 6 to both sides: $6=\frac{3}{4}x$.
Then, multiply both sides by $\frac{4}{3}$ to solve for $x$: $x=6\times\frac{4}{3}=8$.

Step 1: Convert to slope - intercept form ($y = mx + b$)

We start with the equation $\frac{1}{2}y+x=-5$. First, subtract $x$ from both sides: $\frac{1}{2}y=-x - 5$.
Then, multiply both sides by 2 to solve for $y$: $y=-2x-10$.
In the slope - intercept form $y = mx + b$, $m=-2$ and $b = - 10$.

Step 2: Find the x - intercept

The x - intercept is the value of $x$ when $y = 0$. We substitute $y = 0$ into the equation $y=-2x - 10$.
We get $0=-2x-10$.
First, add 10 to both sides: $10=-2x$.
Then, divide both sides by $- 2$: $x=-5$.

Step 1: Convert to slope - intercept form ($y = mx + b$)

We start with the equation $y+\frac{3}{4}x = 6$. Subtract $\frac{3}{4}x$ from both sides: $y=-\frac{3}{4}x + 6$.
In the slope - intercept form $y = mx + b$, $m=-\frac{3}{4}$ and $b = 6$.

Step 2: Find the x - intercept

The x - intercept is the value of $x$ when $y = 0$. We substitute $y = 0$ into the equation $y=-\frac{3}{4}x + 6$.
We get $0=-\frac{3}{4}x+6$.
First, subtract 6 from both sides: $-6=-\frac{3}{4}x$.
Then, multiply both sides by $-\frac{4}{3}$: $x=-6\times(-\frac{4}{3}) = 8$.

Answer:

$m = \frac{3}{4}$, $b=-6$, $x$-intercept $= 8$

Problem 13: $\frac{1}{2}y+x=-5$