Math  /  Algebra

Question4. Write the equation of the line with a slope of 2 and goes thru the point (4,3)(4,3). Hint: use Point Slope form. A. y=2x+5y=2 x+5 B. y=2x5y=-2 x-5 C. y=2x+20y=-2 x+20 y=2x5y=2 x-5

Studdy Solution

STEP 1

What is this asking? We need to find the equation of a line that has a slope of 2 and passes through the point (4,3). Watch out! Don't mix up the *x* and *y* coordinates of the point, and be careful with negative signs when simplifying the equation!

STEP 2

1. Use the Point-Slope Form
2. Simplify to Slope-Intercept Form

STEP 3

The point-slope form of a linear equation is yy1=m(xx1)y - y_1 = m(x - x_1), where mm is the **slope** and (x1,y1)(x_1, y_1) is a **given point** on the line.
This form is super useful because it lets us build a line if we know its slope and *just one point* it passes through.

STEP 4

In our case, the slope mm is **2**, and the given point (x1,y1)(x_1, y_1) is **(4, 3)**.
Let's plug these values into the point-slope form: y3=2(x4)y - 3 = 2(x - 4).
See how we substituted m=2m = 2, x1=4x_1 = 4, and y1=3y_1 = 3?

STEP 5

Let's distribute the **2** on the right side of the equation: y3=2x24y - 3 = 2 \cdot x - 2 \cdot 4, which simplifies to y3=2x8y - 3 = 2x - 8.

STEP 6

To get the equation into slope-intercept form (y=mx+by = mx + b), we need to isolate yy.
We can do this by adding **3** to both sides of the equation: y3+3=2x8+3y - 3 + 3 = 2x - 8 + 3.
This simplifies to y=2x5y = 2x - 5.
Now we have the equation in slope-intercept form, where the slope is **2** and the y-intercept is **-5**.

STEP 7

The equation of the line with a slope of 2 and passing through the point (4,3) is y=2x5y = 2x - 5.
This matches option D!

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