**Title: Writing Equations of Lines** **Instruction:** Write an equation for the graph below in terms of \( x \). **Graph Description:** - The graph appears to show a straight line on a coordinate plane. - The x-axis and y-axis both range from -5 to 5. - The line passes through the point at (-2, 0) and the point at (2, 4). **Line Details:** The line has a positive slope, indicating that as \( x \) increases, \( y \) also increases. **Finding the Equation:** To find the equation of the line, use the slope-intercept form: \[ y = mx + b \] Where: - \( m \) is the slope of the line. - \( b \) is the y-intercept. **Calculating the Slope (\( m \)):** The slope \( m \) is calculated as: \[ m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the points (-2, 0) and (2, 4) into the formula: \[ m = \frac{4 - 0}{2 - (-2)} = \frac{4}{4} = 1 \] **Determining the Y-intercept (\( b \)):** The line intersects the y-axis at the point where \( x = 0 \). Observing the graph, this occurs at: \[ b = 2 \] **Equation of the Line:** Therefore, the equation of the line is: \[ y = x + 2 \] **Input Section:** Use the input box below to enter your equation. **Question Help:** Need assistance? [Message Instructor] **Submission:** Press the "Submit Question" button to submit your answer. **Submit Question: [Button]** --- This exercise helps students practice finding the equation of a line using given points and understanding the relationship between a graph and its algebraic representation.

Q: Solve the equation 5(p-3) = 3(p-2)

A: Given:5p-3=3p-2

Q: Solve 3(k−4)=18

A:

Q: Solve 4 2 x(0) = 6, y(0) = 17 || 13 2 +

A:

Q: Solve: 4. = 4 6. 3

A: find the value of x

Q: Can you solve b for this question! Solve it on paper

A: We have to solve part (b) as asked.

Q: Solve 4 2 x(0) — 2, у(0) - 2 - 17

A:

Q: How do I find the equation for an and solve for s10?

A:

Q: Solve the equation  Y/5 +9=y/2 +18

A: Given equation =>           Y/5 + 9 = Y/2 + 18    * Bring same terms on same side          Y/5  +…

Q: How do I solve the Rooster method in Math?

A: Consider the given information. First, define the roster method. It lists the elements of the…

Q: A = -(B + b)h ; solve for b.

A: The equation is A=12B+bh

Q: V3 - 1 V3 +1

A: To simplify the rational function of the form , multiply both numerator and denominator by…

Q: Solving

A: The given point is,

Q: Solve 2(5-3)+12

A: We will solve the problem

Q: Solve the equation    y-8/5+2=2/5-y/3

A: Given:

Q: Solve  7(a - 4) = 8(a+5)

A: Given, 7a-4 =8a+5  We have to solve the above equation

Q: How do i find the solution to 5p+7=11+4p

A: Given equation

Q: Solve TB +4=AB+2F for B

A: To solve  for .

Q: solve 2s-11 L-1 L. (s-2)²+4

A: We use the standard results of inverse Laplace transform to solve this problem.

Q: Solve them

A: (a)

Q: How do you solve 1 3/10 + 2 2/5

A: Our Aim is to solve (13/10)+(22/5)=?

Q: 32 Solve: +5 %3D х+4 х2-16

A:

Q: 9x-6=4+8x how do I work this problem?

A: First add 6 to both sides

Q: 2x+8y%36 5x+20y=15

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.