Find the Linear Function Equation: Slope 6 Through Point (1,-4)

Q: Why can't I just use y = mx + b directly?

You can use slope-intercept form, but you'd need to find the y-intercept first! Point-slope form is more direct when you have a specific point the line passes through.

Q: What does the negative sign in (1, -4) mean when substituting?

The y-coordinate is negative 4. So $ y - y_1 $ becomes $ y - (-4) = y + 4 $. Remember: subtracting a negative equals adding a positive!

Q: How do I know which form to convert to?

Most problems ask for slope-intercept form $ y = mx + b $ because it's easier to read and graph. Always solve for y as the final step.

Q: Can I check my answer without substituting the point back?

Yes! Check if your equation has the correct slope (coefficient of x should be 6) and see if it makes sense with the given point when you substitute.

Point-Slope Form with Given Coordinates

A linear function with a slope of 6 passes through the point $(1,-4)$ .

Which equation represents the function?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's find the algebraic representation of this function!

00:11 We have a given slope and a point to work with.

00:20 Use the formula for a linear function, Y equals M X plus B.

00:25 Now, substitute the values and solve for B. Take your time!

00:35 Great! Isolate the unknown B to find its value.

00:45 B is the point where our line crosses the Y-axis.

00:52 Plug in the slope and B to write the final function.

01:10 And that's how we solve the problem. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A linear function with a slope of 6 passes through the point $(1,-4)$ .

Which equation represents the function?

Step-by-step solution

To solve the problem, we will determine the equation of a line using the point-slope form. The general formula for a line in point-slope form is:

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

Given the slope $m = 6$ and the point $(1, -4)$ , we can substitute these values into the formula:

$y - (-4) = 6(x - 1)$

Simplifying the equation, we get:

$y + 4 = 6x - 6$

Now, we want to express this in slope-intercept form $y = mx + b$ . So, we solve for $y$ :

$y = 6x - 6 - 4$

Finally, combining like terms gives us the equation:

$y = 6x - 10$

Therefore, the equation that represents the function is $y = 6x - 10$ .

The correct answer choice is:

: $y=6x-10$

Final Answer

$y=6x-10$

Key Points to Remember

Essential concepts to master this topic

Point-Slope Formula: Use $y - y_1 = m(x - x_1)$ with given slope and point
Substitution Technique: Replace m=6, x₁=1, y₁=-4 to get $y + 4 = 6(x - 1)$
Verification Check: Substitute point (1,-4) into final equation: -4 = 6(1) - 10 = -4 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute the slope through parentheses
Don't write y + 4 = 6x - 1 instead of y + 4 = 6x - 6! This happens when you forget to multiply the slope by both terms inside parentheses. Always distribute completely: 6(x - 1) = 6x - 6.

Practice Quiz

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For the function in front of you, the slope is?

FAQ

Everything you need to know about this question

Why can't I just use y = mx + b directly?

You can use slope-intercept form, but you'd need to find the y-intercept first! Point-slope form is more direct when you have a specific point the line passes through.

What does the negative sign in (1, -4) mean when substituting?

The y-coordinate is negative 4. So $y - y_1$ becomes $y - (-4) = y + 4$ . Remember: subtracting a negative equals adding a positive!

How do I know which form to convert to?

Most problems ask for slope-intercept form $y = mx + b$ because it's easier to read and graph. Always solve for y as the final step.

What if I get different answer choices that look similar?

Double-check your arithmetic! Common errors include sign mistakes or forgetting to combine like terms. In this problem: $-6 - 4 = -10$ , not $-2$ .

Can I check my answer without substituting the point back?

Yes! Check if your equation has the correct slope (coefficient of x should be 6) and see if it makes sense with the given point when you substitute.

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