Question

For the given graph,a) Find the slope (m) m=b) Find the y-intercept (b) b= c) Write the equation of the line in slope-intercept form ( I.e. y= max + b ) Y=

Answer 1

`\begin{gathered} a)m=4 \\ b)b=1 \\ c)y=4x+1 \end{gathered}`

Step-by-step explanation

From the given graph;

To determine the slope, recall;

`\begin{gathered} slope(m)=(rise)/(run)=(\Delta y)/(\Delta x) \\ =(y_2-y_1)/(x_2-x_1) \end{gathered}`

a) Substitute the corresponding values of y and x from the graph,

Hence, slope m ;

`\begin{gathered} x_1=1 \\ x_2=2 \\ y_1=1 \\ y_2=5 \\ m=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ =(5-1)/(2-1) \\ =(4)/(1) \\ =4 \end{gathered}`

Given y=mx+b, b = y-intercept; the value of y where the graph intercepts the y-axis and from the graph, the y-intercept is;

`b=1`

c) The equation of the line after substituting the values is;

`\begin{gathered} y=mx+b \\ m=4 \\ b=1 \\ y=4x+1 \end{gathered}`