Question

What is the slope- intercept equation of the line that has a slope of $3$ and $y$ intercept of $7$ ?

Answer 1

Here we simply find the slope-intercept equation by using a slope intercept form of the line.

Complete step-by-step solution:
The slope intercept is the most popular form of a straight line. One can easily describe the characteristics of the straight line even without seeing its graph because the slope and $y$ intercept can easily be identified or read off from this form,
Slope intersection form of the equation of line:
The linear equation of a straight line can be written in the form $y = mx + c$ ---------(1)
This equation is the so-called equation of a straight line that can be drawn on a Cartesian coordinate system in which $y$ is the vertical axis and $x$ is the horizontal axis.
In this equation,we can say that $y$ is how far up the line goes and $x$ is how far along and $m$ is the slope or gradient that this how steep the line is, and finally $c$ is the $y$ intercept that is where the line crosses the $y$ axis.
From our question, we have slope $m = 3$ and $y$ intercept $c = 7$.
On substituting these values in equation(1), we get,
$\Rightarrow y = 3x + 7$
This is the slope- intercept equation of the line.

Note: The slope is positive thus the line is increasing or rising from left to right, but passing through the $y$ axis at point $\left( {0,7} \right)$. For an equation to be in slope-intercept form, the $y$ must be by itself on its side of the equation. If there is a constant right before the $y$, it must be divided out so that $y$ is isolated.