Question

try your best and good luck!

1. write an equation of each line with the given information.

a. slope: 4; y-intercept: -3
b. slo

1. write an equation of each line on the graph.

(graph with points (-2, 3), (1, 1), (4, 4), (0, -4) and grid from -5 to 5 on x and y axes)

Explanation:

Problem 1a

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Substitute values

We are given that the slope $m = 4$ and the y - intercept $b=-3$. Substituting these values into the slope - intercept form, we get $y=4x+( - 3)$ which simplifies to $y = 4x-3$.

Step1: Calculate the slope

The formula for the slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-2,3)$ and $(x_2,y_2)=(1,1)$. Then $m=\frac{1 - 3}{1-( - 2)}=\frac{-2}{3}=-\frac{2}{3}$.

Step2: Use point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(1,1)$ and $m =-\frac{2}{3}$, we have $y - 1=-\frac{2}{3}(x - 1)$.

Step3: Simplify to slope - intercept form

$y-1 =-\frac{2}{3}x+\frac{2}{3}$. Then $y=-\frac{2}{3}x+\frac{2}{3}+1=-\frac{2}{3}x+\frac{2 + 3}{3}=-\frac{2}{3}x+\frac{5}{3}$.

Step1: Calculate the slope

Using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$ with $(x_1,y_1)=(0,-4)$ and $(x_2,y_2)=(4,4)$. Then $m=\frac{4-( - 4)}{4 - 0}=\frac{8}{4}=2$.

Step2: Use slope - intercept form

Since the line passes through $(0,-4)$, the y - intercept $b=-4$. The slope - intercept form is $y=mx + b$. Substituting $m = 2$ and $b=-4$, we get $y = 2x-4$.

Answer:

$y = 4x - 3$

Problem 2 (First line: passing through $(-2,3)$ and $(1,1)$)