Question

graph the line whose equation is given in point slope form.
y - 1 = -\frac{3}{2}(x + 1)
use the graph paper at the end of this packet.

1. choose the equation for a line that passes through (2, -3) and has a slope of m = -4 in point slope form.

a) y - 3 = -4(x - 2)
b) obscured
c) y + 2 = -4(x + 3)
d) y + 3 = -4(x - 2)

1. what is the y - intercept of the following linear equation?

2x + 9y = 18
obscured
a) (9, 0)
b) (9, 2)
c) (0, 2)

1. students, skip this question and go to part 3 (paper - pencil).

teachers, record scores from part 3 here.

Explanation:

Question 8

Step1: Recall Point - Slope Formula

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.

Step2: Identify the values of $x_1,y_1$ and $m$

We are given that the line passes through the point $(2,-3)$ and has a slope $m = - 4$. So, $x_1=2$, $y_1=-3$ and $m=-4$.

Step3: Substitute the values into the point - slope formula

Substitute $x_1 = 2$, $y_1=-3$ and $m=-4$ into $y - y_1=m(x - x_1)$. We get $y-(-3)=-4(x - 2)$, which simplifies to $y + 3=-4(x - 2)$.

Step1: Recall the slope - intercept form

The slope - intercept form of a linear equation is $y=mx + b$, where $b$ is the $y$ - intercept. We need to rewrite the equation $2x+9y = 18$ in slope - intercept form.

Step2: Solve the equation for $y$

Start with $2x+9y=18$. Subtract $2x$ from both sides: $9y=-2x + 18$. Then divide each term by $9$: $y=-\frac{2}{9}x+\frac{18}{9}$, which simplifies to $y =-\frac{2}{9}x + 2$.

Step3: Identify the $y$ - intercept

In the equation $y=-\frac{2}{9}x + 2$, the value of $b$ (the $y$ - intercept) is $2$. The $y$ - intercept is the point where $x = 0$, so the $y$ - intercept is $(0,2)$.

Answer:

D. $y + 3=-4(x - 2)$

Question 9