Answer:
The slope is 4, and the y-intercept is 12.
Step-by-step explanation:
In the given question, the line goes through points (-3,0) and (-2,4).
We need to find the slope and the y-intercept of the line.
Finding Slope:
Slope is [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].
With points (-3,0) and (-2,4):
[tex]m=\frac{4-0}{-2-(-3)}=\frac{4}{1}=4[/tex]
The slope of the line is 4.
Finding y-intercept:
An appropriate equation for what we have so far is:
[tex]y=4x+b[/tex]
We can solve for 'b' to get the y-intercept.
Replace 'x' and 'y' with one of the coordinates and solve for 'b':
[tex]4=4(-2)+b\\4*-2=-8 \leftarrow \text {Distribute}\\4=-8+b\\4+8=-8+8+b \leftarrow \text {Addition Property of Equality} \\\boxed {12=b}[/tex]
The y-intercept is 12.
Final Answer:
The answer should be: "The slope is 4, and the y-intercept is 12."
