Answer:
[tex]y=\frac{6}{5}x+3[/tex] and [tex]y=-\frac{2}{5} x-5[/tex]
Step-by-step explanation:
To find the slope (gradient) of a line, choose 2 points on the line and put their coordinates into the formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
where [tex]m[/tex] is the slope and [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] 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: [tex]m=\frac{3--3}{0--5}=\frac{3+3}{0+5} =\frac{6}{5}[/tex]
This line crosses the y-axis (0, 3) so its y-intercept is 3
Therefore, the equation is [tex]y=\frac{6}{5}x+3[/tex]
The slope of the lower line is: [tex]m=\frac{-5--3}{0--5}=\frac{-5+3}{0+5} =\frac{-2}{5}[/tex]
This line crosses the y-axis (0, -5) so its y-intercept is -5
Therefore, the equation is [tex]y=-\frac{2}{5} x-5[/tex]
