Question

How do you write $5x + y = 4$ in slope-intercept form? What are the slope and y-intercept?

Answer 1

In this question, we will write the given equation in terms of general slope-intercept form by moving x coordinate to the right side, and then by comparison we will find slope and y-intercept of the given line. The slope will be the coefficient of x and y-intercept will be the constant part.

Complete step-by-step answer:
In two-dimensional geometry, the equation of the line in slope-intercept form can be written as,
$y = mx + c$
Where x is the value of x-coordinate, and y is the value of y-coordinate.
Here, m represents the slope of the lines and c represents the y-intercept of the line.
In a line, the slope of the line is the value of the tangent function for the angle which a given line makes with the x-axis in the anticlockwise direction.
And, the y-intercept of a line is the point on the y-axis. The given line intersects the y axis.
Now, the given line in a question is,
$\Rightarrow 5x + y = 4$
Now, subtract $5x$ from both sides,
$\Rightarrow 5x + y - 5x = 4 - 5x$
Simplify the terms,
$\Rightarrow y = - 5x + 4$
So, the equation of the line $5x + y = 4$ in slope-intercept form is $y = - 5x + 4$.
Now, for finding the value of slope and intercept of the given equation we equate above form a given line with standard slope form.
On equating both lines we have $m = - 5$ which imply that the slope of the given line is zero.
Also, the value of ‘c’ of a given line is 4.
This implies that the y-intercept of the given line is 4.

Hence, from above we see that the slope and y-intercept of the given line are -5 and 4 respectively.

Note:
As, we know that there are different forms of line 1st is one point and slope form \left\\{ {y - {y_1} = m\left( {x - {x_1}} \right)} \right\\}, 2nd is two-point form \left\\{ {y - {y_1} = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\left( {x - {x_1}} \right)} \right\\} and 3rd is slope-intercept form \left\\{ {y = mx + c} \right\\}. So, one should be very careful regarding choosing the form of the line which is required in the given question to get slope and y-intercept.