What is the equation of the line that has a slope of -3/4 and passes through point (8,2) ?

2 Answers
Oct 23, 2016

y = -3/4 x +8

Explanation:

Equation of the line with slope of -3/4 and passes through (8,2).

Use the point slope formula where m= slope
and (x_1, y_1) is a point.

y- y_1=m(x-x_1)

y-2= -3/4 (x-8)

This is the equation in point slope form.

If you'd like to express the equation in slope intercept form, distribute the -3/4 across the terms in the parentheses.

y-2= -3/4x -3/4 * -8

y-2 = -3/4 x +6

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y = -3/4 x +8

Oct 23, 2016

y = -\frac{3}{4}x + 8

or

3x + 4y = 32.

Explanation:

First, let's try to connect the question to some concepts that we may be familiar with already. It's important to note that y = mx + b, where m is defined as the \text{slope} and b is defined as the \text{y-intercept}. This also happens to be the \text{slope-intercept form} for the equation of a line! We can use this equation to find our answer.

This question gives you the following information:

\text{1}. m = -\frac{3}{4}

\text{2}. Coordinates (8, 2)

So, how can we use this information to find our answer?

Well, if we use (1), we can rewrite our equation y = mx + b as the following:

y = -\frac{3}{4}x + b.

Note that all I did was replace the m variable with the actual number. Well, we still need to find our b term! We can use (2) to accomplish just that. Input the coordinates (8, 2) into our equation. Since x = 8 and y = 2, we have

2=-\frac{3}{4} \cdot 8 + b = -\frac{24}{4} + b

Luckily for us, 4 divides into -24 perfectly times, leaving us with -6

2 = -6 + b

Adding +6 to both sides (you try this step and see what happens!), we obtain

8 = b.

Hence, our \text{equation of the line} in \text{slope-intercept form} is y = -\frac{3}{4}x + 8. We can also multiply each term by 4 to obtain

4y = -3x + 32 which becomes 3x + 4y = 32 after we add 3x to both sides of the equation.

\text{CHECK}

It's important to note that the equation of the line characterizes the line; that is, every x-value has a unique y-value. We know that when x = 8, we should get y = 2 since (8, 2) is a coordinate on the line. Well, let's plug in x = 8 into our solution and, if we get y = 2, we definitely know we're correct.

Using the slope-intercept form and inputting x = 8, we obtain

y = -\frac{3}{4} \cdot8 + 8 = -6 + 8 = 2.

So, when x = 8, we get y = 2. This verifies that our solution is correct.

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