To get the slope, intercept, and equation of the line
Step 1: We can select two points on the line to get the slope
let's pick points (0,4) and (-2,0)
[tex]\text{slope }=\frac{0\text{ - 4}}{-2\text{ - 0}}=\frac{-4}{-2}=2\text{ }[/tex]
Slope = 2
Step 2: The y-intercept is the point on the line that cuts the y-axis
From the graph, the y-intercept is (0,4)
The x-intercept is the point on the line that cuts the x-axis
From the graph, the x-intercept is (-2,0)
Step 3: picking the points (0,4) and (-2,0)
we can use the formula
[tex]\text{slope =}\frac{y-y_1}{x-x_1}=\text{ }\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\begin{gathered} \frac{y\text{ -4}}{x-0}=\text{ }\frac{0-4}{-2-0} \\ \\ \frac{-4}{-2}\text{ =}\frac{y\text{ - 4}}{x\text{ - 0}} \end{gathered}[/tex]
[tex]\begin{gathered} 2\text{ =}\frac{y\text{ - 4}}{x} \\ \end{gathered}[/tex]
Cross multiplying
2x = y - 4
Re-writing
y = 2x + 4
Equation of the line is
y = 2x + 4
