Question

How do you find the slope and intercept of $f\left( x \right)=5x-7$?

Answer 1

Now first we will try to write the given equation in slope intercept form of line which is given by $y=mx+c$ . Now in the equation m is the slope of the line and c is the y intercept of the line. Hence we can easily find the slope and y intercept of the line.

Complete step by step answer:
Now first let us understand the concept of slope and intercept.
Now firstly any linear equation in two variables gives us a straight line in the XY plane.
Here $f\left( x \right)$ is nothing but y and hence the equation of the line is $y=5x-7$
Now a general equation of a straight line in the XY plane is given by $ax+by+c=0$ .
Now let us first understand the concept of slope.
Slope of a straight line is nothing but the constant value of $\tan \theta$ where $\theta$ is the angle made by the line with x axis. The slope of the line can easily be found by taking the ratio of $\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$ where $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ are the points on the line. Now similarly y intercept is the intersection of line and y axis. Hence we can easily find the y intercept by substituting x = 0 in the equation.
Now we have a general equation for slope point form which is $y=mx+c$ where m is the slope of the line and c is the intercept of the line.
Now consider the given equation $y=5x-7$
We can write the equation as $y=5x+\left( -7 \right)$ .
Now comparing the equation with slope intercept form we get, m = 5 and c = -7.

Hence the slope of the line is 5 and the intercept f the line is – 7.

Note: Now note that we can also plot the graph of the equation by plotting two points on the XY plane. Now once we have the line we can easily find the slope and intercept of the line as intercept is intersection of y axis and line and slope is given by $\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$ where $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ are the points on the line.