Question

How do you find the slope and intercept of $y = 4x - 2$ ?

Answer 1

In this question we need to find the slope and intercept of a line whose equation is given to us. To find the slope and intercept of a line from its equation, we first need to convert the given equation of line into slope-intercept form of straight line. The standard form of equation of line is $y = mx + c$ .

Complete step-by-step solution:
Let us try to find the slope and intercept of a line whose equation is given to us. To find slope and intercept of line we need to convert our given equation into slope-intercept form of straight line. The equation of straight line in slope-intercept form is given by $y = mx + c$ , where $m$ is the slope of line and $c$ is the intercept of line. The slope of a line defines direction and its steepness. The intercept is the point where the line cuts the y-axis.
Equation of the line whose slope and intercept we need to find is $y = 4x - 2$ .
We will first convert the given equation of straight line into slope-intercept form of straight line. Since, the given equation of straight line is already in slope intercept form.
Now, we know that in slope-intercept form of straight line $y = mx + c$ , $m$ is slope and $c$ is the intercept of line.
On comparing the given equation of line $y = 4x - 2$ and its general equation, we get
$m = 4$ And
$c = - 2$
Hence the slope is equal to $4$ and the intercept is equal to $- 2$ for line with equation $y = 4x - 2$ .

Note: Two straight lines are parallel if they same slope and different intercept for, example: $y = mx + {c_1}$ and $y = mx + {c_2}$ where ${c_1} \ne {c_2}$ are parallel. A straight line is perpendicular to $x$ axis and parallel to $y$ axis if its equation is of the form $x = c$ . A straight line is parallel to $x$ axis and perpendicular to $y$ axis if its equation of the form $y = c$ .