Question

How do you write the equation in slope intercept form given point (-1, 6) and has a slope of -3?

Answer 1

Slope intercept form is the general form for linear equations which emphasizes the slope and the y-intercept of the line. The slope intercept form of the equation of the straight line is $y = mx + c$ . So, here we will use the given point in the form of (x, y) and slope in the equation and get the final answer.

Complete step by step answer:
We know that the equation of a line in slope intercept form is given by
$y = mx + c$ …. (1)
Here we have the terms m as the slope and c as the y-intercept.
From the question, it is given that slope is -3, so we can write that $m = - 3$
Substituting m in equation (1) we get,
$\Rightarrow y = - 3x + c$ ….. (2)
We also have the point (1, -6) given to us. It means that x = 1 and y = -6. So, to find c we will substitute x = -1 and y = 6 into equation (2),

\Rightarrow 6 = - 3 \times ( - 1) + c\\\ \Rightarrow 6 = 3 + c \end{array}$$ $$ \Rightarrow c = 3$$ Substituting values of m and c in equation (1) we get, $$y = - 3x + 3$$ Which is the required equation in slope intercept form. **Note:** The slope-intercept is the most popular form of a straight line. It’s useful because of its simplicity. We can easily describe the characteristics of the straight line even without seeing its graph because the slope m and y-intercept can easily be identified or read off from this form. If we plot the graph, we get it as below: