Answered

Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

1) Find the equation of a line with slope [tex]\( m = 3 \)[/tex] that passes through the point [tex]\( (7, 5) \)[/tex]. Write your answer in [tex]\( y = mx + b \)[/tex] form.

Sagot :

GinnyAnswer
To find the equation of a line with a given slope \( m = 3 \) that passes through the point \( (7, 5) \), we can use the point-slope form of a linear equation. The point-slope form is:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope of the line. Here, \( (x_1, y_1) = (7, 5) \) and \( m = 3 \).

Step 1: Write the point-slope form using the given values:

[tex]\[ y - 5 = 3(x - 7) \][/tex]

Step 2: Distribute the slope \( m = 3 \) on the right-hand side:

[tex]\[ y - 5 = 3x - 21 \][/tex]

Step 3: Solve for \( y \) to put the equation into the slope-intercept form \( y = mx + b \):

[tex]\[ y = 3x - 21 + 5 \][/tex]
[tex]\[ y = 3x - 16 \][/tex]

Therefore, the equation of the line in the form \( y = mx + b \) is:

[tex]\[ y = 3x - 16 \][/tex]

The \( y \)-intercept \( b \) is \(-16\).

So, the final equation of the line is:

[tex]\[ y = 3x - 16 \][/tex]
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.