Question

Which equation represents a line that passes through (–2, 4) and has a slope of ?

Answer 1

y – 4 = (x + 2)

Further explanation

We will determine the line equation. Later the equation will be arranged in slope-intercept, point-slope, and standard form.

Given:

• A line that passes through (–2, 4).
• A slope of 1.  

The Process:

• Slope or gradient m = 2.
• Point (x₁, y₁) is (-2, 4).  

Part-1

$\boxed{ \ Slope-intercept \ form: y = mx + c \ }$

Substitution.

$\boxed{ \ \ m = 1 \rightarrow y = x + c \ }$

The line passing through the point (-2, 4).

$\boxed{ \ x_1 = -2, y_1 = 4 \ } \rightarrow \boxed{ \ 4 = (-2) + c \ } \rightarrow \boxed{ \ c = 6 \ }$

Thus the slope-intercept form is $\boxed{\boxed{ \ y = x + 6 \ }}$

Part-2

$\boxed{ \ Point-slope \ form: y - y_1 = m(x - x_1) \ }$

$\boxed{ \ m = 1 \rightarrow y - y_1 = (x - x_1) \ }$

The line passing through the point (-2, 4).

$\boxed{ \ x_1 = -2, y_1 = 4 \ } \rightarrow \boxed{ \ y - 4 = (x - (-2)) \ }$

Thus the point-slope form is $\boxed{\boxed{ \ y - 4 = (x + 2) \ }}$

Part-3

$\boxed{ \ Standard \ form: ax + by = k \ }$

From the results of Part-1, we set the position of the variables.

$\boxed{ \ y = x + 6 \ }$

$\boxed{ \ x + 6 = y \ }$

$\boxed{ \ x - y = - 6 \ }$

Thus the standard form is $\boxed{\boxed{ \ x - y = - 6 \ }} \ or \ \boxed{\boxed{ \ y - x = 6 \ }} \ or \ \boxed{\boxed{ \ x - y + 6 = 0 \ }}$

Learn more

1. Find out ordered pairs could be points on a line that is perpendicular to another line  brainly.com/question/2601054  
2. Determine the line equation, in slope-intercept form, that is parallel to the given line and passes through a point  brainly.com/question/1473992  
3. Determine an equation represents Nolan’s line brainly.com/question/2657284

Keywords: the line equation, slope-intercept form, standard form, point-slope, gradien, a line that passes through (–2, 4)

Answer 2

Slope = 1

equation
y - y1 = m(x - x =1)
a line that passes through (–2, 4)
so equation should be

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

answer is first one.

y – 4 = (x + 2)