Answer:
a. Slope intercept form: [tex]y= 4x +11[/tex]
b. The y intercept is 11
c. The x intercept is [tex]-\frac{11}{4}[/tex]
d. Standard Form: [tex]y - 4x = 11[/tex]
e. See attachment for graph
Explanation:
Given
Slope (m)
[tex]m = 4[/tex]
[tex](x_1,y_1) = (-2,3)[/tex]
Solving (a): The line equation in slope intercept
This is solved using:
[tex]y - y_1 = m(x - x_1)[/tex]
Substitute values for y1, x1 and m
[tex]y - 3 = 4(x - (-2))[/tex]
[tex]y - 3 = 4(x +2)[/tex]
[tex]y - 3 = 4x +8[/tex]
Add 3 to both sides
[tex]y - 3 +3= 4x +8 + 3[/tex]
[tex]y= 4x +11[/tex]
Solving (b): The y intercept
To do this, we simply take x as 0.
Substitute 0 for x in [tex]y= 4x +11[/tex]
[tex]y = 4(0) + 11[/tex]
[tex]y = 0 + 11[/tex]
[tex]y = 11[/tex]
The y intercept is 11
Solving (c): The x intercept
To do this, we simply take y as 0.
Substitute 0 for y in [tex]y= 4x +11[/tex]
[tex]0 = 4x + 11[/tex]
Collect Like Terms
[tex]4x=0-11[/tex]
[tex]4x=-11[/tex]
Solve for x
[tex]x = -\frac{11}{4}[/tex]
The x intercept is [tex]-\frac{11}{4}[/tex]
The y intercept is 11
d. The equation in standard form
Equation in standard form is written in the following format: [tex]Ax + By = c[/tex]
[tex]y= 4x +11[/tex]
Subtract 4x from both sides
[tex]y - 4x = 4x - 4x + 11[/tex]
[tex]y - 4x = 11[/tex]
Hence, the equation in standard form is [tex]y - 4x = 11[/tex]
e. The graph
We have that:
[tex](-2,3)[/tex] ---- given
In (b), we calculated the y intercept to be 11.
This implies that: [tex](0,11)[/tex]
So, we can plot the graph through [tex](0,11)[/tex] and [tex](-2,3)[/tex]
See attachment for graph
