Question

Wright in point-slope form, slope-intercept form and in standard form an equation that passes through (-1, 2) with slope 4

Answer 1

Answer:

$\textsf{Point-slope form}: \quad \sf y-2=4(x+1)$

$\textsf{Slope-intercept form}: \quad \sf y=4x+6$

$\textsf{Standard form}: \quad \sf 4x-y=-6$

Step-by-step explanation:

Given information:

• Slope = 4
• Point on line = (-1, 2)

Point-slope form of linear equation:  

$\sf y-y_1=m(x-x_1)$

(where m is the slope and (x₁, y₁) is a point on the line)

Substitute the given slope and point into the formula:

$\implies \sf y-2=4(x-(-1))$

$\implies \sf y-2=4(x+1)$

Slope-intercept form of a linear equation:

$\sf y=mx+b$

(where m is the slope and b is the y-intercept)

Substitute the given slope and point into the formula and solve for b:

$\implies \sf 2=4(-1)+b$

$\implies \sf b=6$

Therefore:

$\sf y=4x+6$

Standard form of a linear equation:

$\sf Ax+By=C$

(where A, B and C are constants and A must be positive)

Rearrange the found slope-intercept form of the equation into standard form:

$\implies \sf y=4x+6$

$\implies \sf 4x-y+6=0$

$\implies \sf 4x-y=-6$

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Answer 2

Point-slope form

$y-2=4(x+1)$

Slope-intercept form

$y-2=4x+4 \\ \\ y=4x+6$

Standard form

$4x-y+6=0$