Answer:
[tex]y=\frac{1}{4}x-2[/tex]
Explained Answer:
[tex]\text{Here we need to find the equation of the line shown in the graph using slope}\\\text{intercept form. The equation of a line in slope intercept form is given by:}\\y=mx+b\\\text{where, }m\text{ is the slope of the line and }b\text{ is the y-intercept.}\\\text{You will always need at least two points through which a line passes to find}\\\text{its equation. Let those two points be }(x_1,y_1)\text{ and }(x_2,y_2).[/tex]
[tex]\text{Then you may write the formula for the slope as:}\\\text{slope(m) = }\frac{y_2-y_1}{x_2-x_1}.[/tex]
[tex]\text{Now coming back to your question, take any two points through which the }\\\text{given line passes:}\\(x_1,y_1)=(0,-2)\\(x_2,y_2)=(8,0)[/tex]
[tex]\text{Now find the slope of the line by using the formula.}\\\text{Slope(m)}=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-2)}{8-0}=2/8=1/4[/tex]
[tex]\text{y-intercept}(b)=-2.\\\text{(The y-intercept is the y-value of the point where a line or a curve intersect at}\\\text{y-axis. For example in this case, the line given in the graph intersects y-axis}\\\text{at (0,-2). The y-value of this point, i.e. -2 is the y-intercept of the line.)}[/tex]
[tex]\text{Now the equation of the line is given by:}\\y=mx+b\\\text{or, }y=(1/4)x+(-2)\\\therefore\ y=\frac{1}{4}x-2\text{ is the required equation of the line.}[/tex]
Real Solution:
[tex]\text{Solution: }\\\text{Let }(x_1,y_1)=(0,-2)\text{ and }(x_2,y_2)=(8,0).\\\text{Using slope formula,}\\\text{Slope(m) = }\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-2)}{8-0}=\frac{2}{8}=\frac{1}{4}\\\\\text{Also, y-intercept}(b)=-2[/tex]
[tex]\text{Now the equation of the line is given by:}\\y=mx+b\\\text{or, }y=\frac{1}{4}x+(-2)\\\text{or, }y=\frac{1}{4}x-2[/tex]
[tex]\text{Now let's take another coordinate from the graph, say (-8,-4). }\\\text{Put }x=-8\text{ and }y=-4\text{ in the equation,}\\-4=\frac{1}{4}(-8)-2\\\\\text{or, }-4=-2-2\\\text{or, }-4=-4\text{ (True)}\\\text{So, the coordinate perfectly fits into our function/equation.}[/tex]
