Find the equation of the line passing through the points (2,4) and (5,13).

Step 1: Calculate the gradient (m) of the line using the given points A(2,4) and B(5,13). The formula for the gradient is m = (y₂ − y₁)/(x₂ − x₁). m = (13 − 4)/(5 − 2) = 9/3 = 3; Step 2: Use the point-slope form of a linear equation, y − y₁ = m(x − x₁), or substitute one of the points and the gradient into y = mx + c to find the y-intercept (c). Using point A(2,4): 4 = 3(2) + c; 4 = 6 + c; c = 4 − 6; c = −2; Step 3: Write the equation of the line in the form y = mx + c. y = 3x − 2; The equation of the line is y = 3x − 2.

Find the equation of the line passing through the points (2,4) and (5,13).

Step 1: Calculate the gradient (m) of the line using the given points A(2,4) and B(5,13). The formula for the gradient is m = (y₂ − y₁)/(x₂ − x₁). m = (13 − 4)/(5 − 2) = 9/3 = 3; Step 2: Use the point-slope form of a linear equation, y − y₁ = m(x − x₁), or substitute one of the points and the gradient into y = mx + c to find the y-intercept (c). Using point A(2,4): 4 = 3(2) + c; 4 = 6 + c; c = 4 − 6; c = −2; Step 3: Write the equation of the line in the form y = mx + c. y = 3x − 2; The equation of the line is y = 3x − 2.

Solved: Find the equation of the line passing through the…

Calculate the gradient ( $m$ ) of the line using the given points A $(2,4)$ and B $(5,13)$ .
The formula for the gradient is $m = \frac{y_2 - y_1}{x_2 - x_1}$ .
$m = \frac{13 - 4}{5 - 2} = \frac{9}{3} = 3$
Use the point-slope form of a linear equation, $y - y_1 = m(x - x_1)$ , or substitute one of the points and the gradient into $y = mx + c$ to find the y-intercept ( $c$ ).
Using point A $(2,4)$ :
$4 = 3(2) + c$ $4 = 6 + c$ $c = 4 - 6$ $c = -2$
Write the equation of the line in the form $y = mx + c$ .
$y = 3x - 2$

Find the equation of the line passing through the points (2,4) and (5,13).

Answer

Step-by-step solution

Calculate the gradient ( $m$ ) of the line using the given points A $(2,4)$ and B $(5,13)$ .

Use the point-slope form of a linear equation, $y - y_1 = m(x - x_1)$ , or substitute one of the points and the gradient into $y = mx + c$ to find the y-intercept ( $c$ ).

Write the equation of the line in the form $y = mx + c$ .

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Find the equation of the line passing through the points (2,4) and (5,13).

Answer

Step-by-step solution

Calculate the gradient (mmm) of the line using the given points A(2,4)(2,4)(2,4) and B(5,13)(5,13)(5,13).

Use the point-slope form of a linear equation, y−y1=m(x−x1)y - y_1 = m(x - x_1)y−y1​=m(x−x1​), or substitute one of the points and the gradient into y=mx+cy = mx + cy=mx+c to find the y-intercept (ccc).

Write the equation of the line in the form y=mx+cy = mx + cy=mx+c.

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Still stuck on this one?

More Mathematics Questions

Calculate the gradient ( $m$ ) of the line using the given points A $(2,4)$ and B $(5,13)$ .

Use the point-slope form of a linear equation, $y - y_1 = m(x - x_1)$ , or substitute one of the points and the gradient into $y = mx + c$ to find the y-intercept ( $c$ ).

Write the equation of the line in the form $y = mx + c$ .