Find the equation of a line with gradient 3 that passes through the point (2, 1).

Step 1: Identify the given information. The gradient (slope) m = 3. The line passes through the point (x₁, y₁) = (2, 1). Step 2: Use the point-slope form of a linear equation, which is y − y₁ = m(x − x₁). Substitute the given values into the formula: y − 1 = 3(x − 2); Step 3: Simplify the equation to the slope-intercept form y = mx + c. Distribute the gradient on the right side: y − 1 = 3x − 6 Add 1 to both sides of the equation: y = 3x − 6 + 1; y = 3x − 5; The equation of the line is y = 3x − 5. y = 3x − 5

Find the equation of a line with gradient 3 that passes through the point (2, 1).

Step 1: Identify the given information. The gradient (slope) m = 3. The line passes through the point (x₁, y₁) = (2, 1). Step 2: Use the point-slope form of a linear equation, which is y − y₁ = m(x − x₁). Substitute the given values into the formula: y − 1 = 3(x − 2); Step 3: Simplify the equation to the slope-intercept form y = mx + c. Distribute the gradient on the right side: y − 1 = 3x − 6 Add 1 to both sides of the equation: y = 3x − 6 + 1; y = 3x − 5; The equation of the line is y = 3x − 5. y = 3x − 5

Solved: Find the equation of a line with gradient 3 that…

Identify the given information.
The gradient (slope) $m = 3$ .
The line passes through the point $(x_1, y_1) = (2, 1)$ .
Use the point-slope form of a linear equation, which is $y - y_1 = m(x - x_1)$ .
Substitute the given values into the formula:
$y - 1 = 3(x - 2)$
Simplify the equation to the slope-intercept form $y = mx + c$ .
Distribute the gradient on the right side:
$y - 1 = 3x - 6$
Add 1 to both sides of the equation:
$y = 3x - 6 + 1$ $y = 3x - 5$
The equation of the line is y = 3x - 5.

Find the equation of a line with gradient 3 that passes through the point (2, 1).

Answer

Step-by-step solution

Identify the given information.

Use the point-slope form of a linear equation, which is $y - y_1 = m(x - x_1)$ .

Simplify the equation to the slope-intercept form $y = mx + c$ .

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Find the equation of a line with gradient 3 that passes through the point (2, 1).

Answer

Step-by-step solution

Identify the given information.

Use the point-slope form of a linear equation, which is y−y1=m(x−x1)y - y_1 = m(x - x_1)y−y1​=m(x−x1​).

Simplify the equation to the slope-intercept form y=mx+cy = mx + cy=mx+c.

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Still stuck on this one?

More Mathematics Questions

Use the point-slope form of a linear equation, which is $y - y_1 = m(x - x_1)$ .

Simplify the equation to the slope-intercept form $y = mx + c$ .