Answer:
[tex]y=\frac{3}{5}x+1[/tex]
Step-by-step explanation:
Given:
A line with two points on it. The points are:
[tex](x_1,y_1)=(-5,-2)\\\\(x_2,y_2)=(5,4)[/tex]
The slope-intercept form of the equation of a line is given as:
[tex]y=mx+b[/tex]
Where 'm' is the slope of the line and 'b' is the y-intercept.
The slope of a line with two points [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex] on it is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Plug in the given values and solve for 'm'. This gives,
[tex]m=\frac{4-(-2)}{5-(-5)}\\\\ m=\frac{4+2}{5+5}\\\\m=\frac{6}{10}\\\\m=\frac{3}{5}[/tex]
Now, y-intercept is the value of 'y' where 'x' is 0 or the point where the line crosses the y axis.
From the graph, the line cuts the y-axis at the point (0, 1).
Therefore, the y-intercept is, [tex]b=1[/tex]
Hence, the equation of the line is given as:
[tex]y=mx+b\\\\y=\frac{3}{5}x+1[/tex]
