Question

Y=2x+ 7 in point-slope form

Answer 1

• y - 7 = 2(x - 0)

Solution :

We know that,

• 
  `point \: slope : y – y1 = m(x – x1)`

where,

• m = slope of the line
• (x1, y1) = Points through which the line passes

ATQ,

• y = 2x + 7

where,

• m = 2
• 7 = y intercept

Therefore,

• 
  `point \: slope \: = (y - 7) = 2(x - 0) \\`
• 
  `point \: slope \: = (y - 7) = 2(x - 0)`

Thus, the point slope form of y = 2x + 7 would be y - 7 = 2(x -0).

Answer 2

`y - 7 = 2(x - 0)`

Explanation:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. Therefore, for the equation y = 2x + 7:

• Slope: m = 2
• y-intercept: b = 7

The point-slope form of a linear equation is y - y₁ = m(x - x₁), where (x₁, y₁) represents a point on the line, and m is the slope of the line.

To write the equation y = 2x + 7 in point-slope form, we need to identify a point (x₁, y₁) on the line and the slope (m) of the line.

We already know that the slope is m = 2.

The y-intercept is the point where the line crosses the y-axis, so when x = 0. Therefore, as we know that the y-intercept is 7, we can write this as point (0, 7).

Substitute the slope (m = 2) and the point on the line (0, 7) into the point-slope formula:

`y - y_1 = m(x - x_1)`

`y - 7 = 2(x - 0)`

Therefore, y = 2x + 7 in point-slope form is:

`\large\boxed{\boxed{y - 7 = 2(x - 0)}}`