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!

Question

asked Feb 12, 2023 126k views

2 Answers

Broatian · Answer 1 · 2023-02-17T19:34:55+0000

Answer:

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
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