STEP - BY - STEP EXPLANATION
What to find?
The slope- intercept equation of line 1, 2, 3 and 4.
Given:
To find- the slope - intercept equation, we will be following the steps below:
Step 1
Identify any two points on the line.
Step 2
Find the slope of the line using the formula;
[tex]slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]
Step 3
Find the intercept of the line using the slope in step 1 and any point on the line.
Step 4
Form the equation by substituting the slope and intercept into the formula y=mx + c
That is;
Line 1
(-3, -2) and (0, -3)
x₁ = -3 y₁=-2
x₂=0 y₂=-3
[tex]slope(m)=\frac{-3-(-2)}{0-(-3)}=\frac{-1}{3}=-\frac{1}{3}[/tex]
Observe that line 1 cut across the y-axis at y=-3
Hence, the y-intercept (b) = -3
The equation of line 1 is:
[tex]y=-\frac{1}{3}x-3[/tex]
Line 2
(-2, -2) and (0, 0)
x₁ = -2 y₁=-2
x₂=0 y₂=0
[tex]slope(m)=\frac{0+2}{0+2}=\frac{2}{2}=1[/tex]
Line 2 passes through the origin, this implies that the y-intercept is 0.
Hence, the equation of line 2 is y= x
Line 3
ANSWER
Line 1 D: -1/3 x - 3
Line 2 I: y=x
