Question

The solution to the system is at (-5, -3). Write the equations of the lines that is shown in slope-intercept form (y=mx+b). Answer requires two equations, please help!

Answer 1

#1

• (0,3)
• (-5,-3)

Slope

• m=(-3-3)/-5
• m=6/5

Equation

• y=6/5x+3

#2

• (0,-5)
• (-5,-3)

Slope

• m=(-3+5)/-5
• m=-2/5

Equation

• y=-2/5x-5

Answer 2

`y=(6)/(5)x+3` and
`y=-(2)/(5) x-5`

Explanation:

To find the slope (gradient) of a line, choose 2 points on the line and put their coordinates into the formula:
`m=(y_2-y_1)/(x_2-x_1)`

where
`m` is the slope and
`(x_1,y_1)` and
`(x_2,y_2)` are the 2 points.

The y-intercept is the y-coordinate of the point where the line crosses the y-axis.

The question has given you one point that both lines pass through: (-5, -3)

You also need to determine the points where both lines cross the y-axis to determine their y-intercepts - use those as the second points.

From inspection, for the upper line this is (0, 3) and for the other line this is (0, -5)

Therefore, the slope of the upper line is:
`m=(3--3)/(0--5)=(3+3)/(0+5) =(6)/(5)`

This line crosses the y-axis (0, 3) so its y-intercept is 3

Therefore, the equation is
`y=(6)/(5)x+3`

The slope of the lower line is:
`m=(-5--3)/(0--5)=(-5+3)/(0+5) =(-2)/(5)`

This line crosses the y-axis (0, -5) so its y-intercept is -5

Therefore, the equation is
`y=-(2)/(5) x-5`