Question

How do you find the slope of the line $y = 3.78x - 4$?

Answer 1

First, we will figure out what type of formula should be used. Here, we know that the line is in the form of slope-intercept form. Every equation that is in this form has a slope ‘m’. So, after that we will find the slope from the help of the slope-intercept form.

Complete step by step answer:
To find the slope, first we have to convert the equation in a slope-intercept form. The slope-intercept form is:
$y = mx + c$
We can see that the question is already in the slope-intercept form. So, to find the slope, we just have to identify the term from the slope-intercept form which is known as the slope.
Here, from this slope-intercept form we get that the coefficient of ‘x’ is ‘m’ and m= slope. Here, c= y-intercept.
According to the slope-intercept formula, we get that:
$m = 3.78$and $c = - 4$
Therefore, we get that the slope of the line $y = 3.78x - 4$is $3.78$.

Additional information:
Slope in Mathematics means the ratio of rate of change of values of x and values of y. If we write the formula of slope, then we write it as ${\text{slope = }}\dfrac{{{\text{rate}}\,{\text{of}}\,{\text{change}}\,{\text{in}}\,{\text{values}}\,{\text{of}}\,{\text{y}}}}{{{\text{rate}}\,{\text{of}}\,{\text{change}}\,{\text{in}}\,{\text{values}}\,{\text{of}}\,{\text{x}}}}$. The formula can be written as $m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$. Slope is also represented as ${\text{slope = }}\dfrac{{{\text{rise}}}}{{{\text{run}}}}$. Slope is expressed as rise over run.

Note: Slope is actually the steepness of a line. If a line is aligned or positioned from the bottom left to upper right, then the slope is a positive slope. If a line is aligned from upper left to bottom right, then the slope is a negative slope.