1) y-intercept is: y = 1
Slope = 2/5
Equation is: y = (2/5)x + 1
2) y-intercept is: y = 0
Slope = 3/2
Equation is: y = (3/2)x
3) y-intercept is: y = -2
Slope = 1/2
Equation is: y = (1/2)x - 2
4) y-intercept is: y = -1
Slope = 4/3
Equation is: y = (4/3)x - 1
5) y-intercept is : y = 3
Slope = 3/-3 = -1
Equation is: y = -x + 3
6) y-intercept is: y = 1
Slope = 3/4
Equation is: y = (3/4)x + 1
How to find the slope and y-intercept?
The general form for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
The formula for the slope between two coordinates is:
m = (y₂ - y₁)/(x₂ - x₁)
1) y-intercept is the point where the line intersects the y-axis which is:
y = 1
Using the coordinates (-2, -2) and (3, 0), we have:
Slope = (0 + 2)/(3 + 2)
Slope = 2/5
Equation is:
y = (2/5)x + 1
2) y-intercept is the point where the line intersects the y-axis which is:
y = 0
Using the coordinates (0, 0) and (2, 3), we have:
Slope = (3 - 0)/(2 - 0)
Slope = 3/2
Equation is:
y = (3/2)x
3) y-intercept is the point where the line intersects the y-axis which is:
y = -2
Using the coordinates (-3, -1) and (3, 2), we have:
Slope = (2 + 1)/(3 + 3)
Slope = 3/6 = 1/2
Equation is:
y = (1/2)x - 2
4) y-intercept is the point where the line intersects the y-axis which is:
y = -1
Using the coordinates (0, -1) and (3, 3), we have:
Slope = (3 + 1)/(3 - 0)
Slope = 4/3
Equation is:
y = (4/3)x - 1
5) y-intercept is the point where the line intersects the y-axis which is:
y = 3
Using the coordinates (3, 0) and (0, 3), we have:
Slope = (3 - 0)/(0 - 3)
Slope = 3/-3 = -1
Equation is:
y = -x + 3
6) y-intercept is the point where the line intersects the y-axis which is:
y = 1
Using the coordinates (0, 1) and (4, 4), we have:
Slope = (4 - 1)/(4 - 0)
Slope = 3/4
Equation is:
y = (3/4)x + 1