Question

How do you find the slope and intercept of $y = - 5x + 2$ ?

Answer 1

Hint : In this question we have to write the slope and intercept of $y = - 5x + 2$ . We know that the equation which is in the slope intercept will be in the form like $y = mx + b$ . Then, to determine the $y$ -intercept, let us assume $x = 0$ and solve for $y$ and to determine the $x$ -intercept, let us assume $y = 0$ and solve for $x$ . Then, we will determine the slope using the formula, $m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$ .

Complete step-by-step answer :
Here, we have to write the slope and intercept of $y = - 5x + 2$ .
The equation in slope intercept form will be like $y = mx + b$ , where $m$ is the slope of the line and $b$ is the $y$ -intercept of the line, or the $y$ -coordinate if the point at which the line crosses the $y$ -axis.
Now, to determine the $x$ -intercept, let us assume $y = 0$ and solve for $x$ .
Thus, we have,
$0 = - 5x + 2$
$5x = 2$
$x = \dfrac{2}{5}$
Hence, the $x$ -intercept of $y = - 5x + 2$ is at $\left( {\dfrac{2}{5},0} \right)$ .
Now, to determine the $y$ -intercept, let us assume $x = 0$ and solve for $y$ .
Thus, we have,
$y = - 5\left( 0 \right) + 2$
$y = 2$
Hence, the $y$ -intercept of $y = - 5x + 2$ is at $\left( {0,2} \right)$ .
Thus, the two points are $\left( {\dfrac{2}{5},0} \right)$ and $\left( {0,2} \right)$ .
We know that the slope can be written as, $m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$ .
$m = \dfrac{{2 - 0}}{{0 - \dfrac{2}{5}}}$
$m = - \dfrac{2}{2} \times \dfrac{5}{1}$
$m = - 5$
Hence, the slope of $y = - 5x + 2$ is $- 5$ .
So, the correct answer is “ $m = - 5$ ”.

Note : In this question it is important to note here that $y = mx + b$ is the form called the slope-intercept form of the equation of the line. It is the most popular form of straight line. Many find this as useful because of its simplicity. One can easily describe the characteristics of the straight line even without seeing its graph because the slope and $y$ -intercept can easily be defined or read off from this form. The slope $m$ measures how steep the line is with respect to the horizontal. Let us consider two points $\left( {{x_1},{y_1}} \right)$ and $\left( {{x_2},{y_2}} \right)$ found in the line, the slope can be written as, $m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$ . The $y$ -intercept $b$ is the point where the line crosses the $y$ -axis.