Write the equation of the function with slope 2 passing through the point (2,5). Determine the x-intercept…

Question

Write the equation of the function with slope 2 passing through the point (2,5). Determine the x-intercept and y-intercept of the function f(x) = −x + 6.

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Here are the solutions for questions 6 and 7. Question 6: Write the equation of the function with slope 2 passing through the point (2,5). Step 1: Use the point-slope form of a linear equation, y − y₁ = m(x − x₁). Given slope m = 2 and point (x₁, y₁) = (2, 5). Step 2: Substitute the given values into the point-slope form. y − 5 = 2(x − 2); Step 3: Distribute the slope and solve for y to get the equation in slope-intercept form, y = mx + b. y − 5 = 2x − 4; y = 2x − 4 + 5; y = 2x + 1; The equation of the function is y = 2x + 1. Question 7: Determine the x-intercept and y-intercept of the function f(x) = −x + 6. Step 1: To find the x-intercept, set f(x) = 0 and solve for x. 0 = −x + 6; x = 6 The x-intercept is (6, 0). Step 2: To find the y-intercept, set x = 0 and solve for f(x). f(0) = −(0) + 6; f(0) = 6 The y-intercept is (0, 6).

Write the equation of the function with slope 2 passing through the point (2,5). Determine the x-intercept and y-intercept of the function f(x) = -x + 6.

Answers

Step-by-step solution

Part 6· 3 steps

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

Substitute the given values into the point-slope form.

Distribute the slope and solve for $y$ to get the equation in slope-intercept form, $y = mx + b$ .

Part 7· 2 steps(6, 0)

To find the x-intercept, set $f(x) = 0$ and solve for $x$ .

To find the y-intercept, set $x = 0$ and solve for $f(x)$ .

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