How to find the slope of a line - GRE Quantitative Reasoning

The equation of a line is:

y = mx + b, where m is the slope

4_x_ – 16_y_ = 24

–16_y_ = –4_x_ + 24

y = (–4_x_)/(–16) + 24/(–16)

y = (1/4)x – 1.5

Slope = 1/4

Solve equation for y. y=mx+b, where m is the slope

We can convert the given equation into slope-intercept form, y=mx+b, where m is the slope. We get y = (-1/2)x + (-7/2)

Put the equation in slope-intercept form:

y = mx + b

-2y = -6x +14

y = 3x – 7

The slope of the line is represented by M; therefore the slope of the line is 3.

One can use either the slope formula m = (y2 – y1)/(x2 – x1) or the standard line equation, y = mx + b to solve for the slope, m. By calculation or observation, one can determine that the slope is –3.

First put the question in slope intercept form (y = mx + b):

–(1/6)y = –(14/3)x – 7 =>

y = 6(14/3)x – 7

y = 28x – 7.

The slope is 28.

First put the equation into slope-intercept form, solving for y: 2x – 4y = 10 → –4y = –2x + 10 → y = 1/2*x – 5/2. So the slope is 1/2.

Slope is found by dividing the difference in the y-coordinates by the difference in the x-coordinates.

$\frac{(12-7)}{(4-3)}$=\frac{5}{1}$=5

The slope is equal to the difference between the y-coordinates divided by the difference between the x-coordinates.

Use the give points in this formula to calculate the slope.

To rearrange the equation into a y=mx+b format, you want to isolate the y so that it is the sole variable, without a coefficient, on one side of the equation.

First, add 11x to both sides to get 6y=7+16x .

Then, divide both sides by 6 to get y=\frac{7+16x}{6}$ .

If you divide each part of the numerator by 6, you get y=\frac{7}{6}$+\frac{16x}{6}$ . This is in a y=b+mx form, and the m is equal to $\frac{16}{6}$, which is reduced down to $\frac{8}{3}$ for the correct answer.

To find the slope, put the equation in slope-intercept form . In this case we have y=-$\frac{3}{2}$+5, which indicates that the slope is .

The slope is equal to the difference between the y-coordinates divided by the difference between the x-coordinates.

Use the give points in this formula to calculate the slope.

To find the slope of a line, you should convert an equation to the slope-intercept form. In this case, the equation would be , which means the slope is .

A question like this is actually rather easy. All you need to do is rewrite the equation in slope intercept form, that is:

Therefore, begin to simplify:

Becomes...

Then...

Finally, divide both sides by :

The coefficient for the term is your slope:

Since the equation is defined as it is, you know the y-intercept is . This is the point . To find the slope of the line, you merely need to use the two points that you have and find the equation:

There are two key facts to register about this drawing. First, the line clearly has a negative slope, given that it runs "downhill" when you look at it from left to right. Secondly, it has a positive y-intercept. Therefore, you know that the coefficient for the term must be negative, and the numerical coefficient for the y-intercept must be positive. This only occurs in the equation . Therefore, this is the only viable option.

We should put this equation in the form of y = mx + b, where m is the slope.

We start with 4_x_ + 3_y_ = 7.

Isolate the y term: 3_y_ = 7 – 4_x_

Divide by 3: y = 7/3 – 4/3 * x

Rearrange terms: y = –4/3 * x + 7/3, so the slope is –4/3.

The equation of a line is:

y = mx + b, where m is the slope

4_x_ – 16_y_ = 24

–16_y_ = –4_x_ + 24

y = (–4_x_)/(–16) + 24/(–16)

y = (1/4)x – 1.5

Slope = 1/4

Solve equation for y. y=mx+b, where m is the slope