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Math  /  Algebra

QuestionThe straight line shown below passes through the points (6,4)(6,4) and (11,49)(11,49).
What is the gradient of this line? Give your answer as an integer or as a fraction in its simplest form.

Studdy Solution

STEP 1

1. We are given two points on a straight line: (6,4) (6,4) and (11,49) (11,49) .
2. We need to find the gradient (slope) of the line passing through these points.
3. The gradient is calculated as the change in y y divided by the change in x x .

STEP 2

1. Identify the coordinates of the given points.
2. Use the formula for the gradient of a line.
3. Simplify the expression to find the gradient.

STEP 3

Identify the coordinates of the given points. The first point is (x1,y1)=(6,4) (x_1, y_1) = (6, 4) and the second point is (x2,y2)=(11,49) (x_2, y_2) = (11, 49) .

STEP 4

Use the formula for the gradient of a line, which is given by:
m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1}
Substitute the values from the points into the formula:
m=49−411−6 m = \frac{49 - 4}{11 - 6}

STEP 5

Simplify the expression to find the gradient.
Calculate the difference in the y y -coordinates:
49−4=45 49 - 4 = 45
Calculate the difference in the x x -coordinates:
11−6=5 11 - 6 = 5
So, the gradient m m is:
m=455 m = \frac{45}{5}
Simplify the fraction:
m=9 m = 9
The gradient of the line is:
9 \boxed{9}

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